To treat a burn on your hand, you decide to place an ice cube on the burned skin. The mass of the ice cube is 13.2 g, and its initial temperature is -11.9 °C. The water resulting from the melted ice reaches the temperature of your skin, 30.0 °C. How much heat is absorbed by the ice cube and resulting water? Assume that all the water remains in your hand
Q=Q₁+Q₂+Q₃ = c₁mΔT₁+ λm + c₂mΔT₂=
= m(c₁ΔT₁ + λ+c₂ΔT)=
=0.0132(2060•11.9+ 335000+4183•30)=
=0.0132(24514+335000+125490)=
=6402 J
To determine the amount of heat absorbed by the ice cube and the resulting water, you'll need to use the formula:
Q = mcΔT
Where:
Q represents the amount of heat absorbed or released
m is the mass of the substance (in this case, the ice and water)
c is the specific heat capacity of the substance
ΔT is the change in temperature
Let's calculate the amount of heat absorbed by the ice cube and the resulting water step by step:
1. Calculate the heat absorbed by the ice cube:
We know:
Mass of the ice cube (m) = 13.2 g
Initial temperature (T1) = -11.9 °C
Final temperature (T2) = 0 °C (since the ice cube melts at 0 °C)
To find the heat absorbed by the ice cube, we need to calculate the change in temperature (ΔT):
ΔT = T2 - T1
ΔT = 0 °C - (-11.9 °C)
ΔT = 11.9 °C
Next, we need to know the specific heat capacity of ice (c). The specific heat capacity of ice is 2.09 J/g°C.
Now, we can calculate the heat absorbed by the ice cube:
Q = mcΔT
Q = 13.2 g * 2.09 J/g°C * 11.9 °C
2. Calculate the heat absorbed by the resulting water:
We know:
Mass of the water (m) = mass of the ice cube (13.2 g) since all the water remains in your hand
Initial temperature (T1) = 0 °C (the melting point of ice)
Final temperature (T2) = 30.0 °C (the temperature of your skin)
Again, we need to calculate the change in temperature (ΔT):
ΔT = T2 - T1
ΔT = 30.0 °C - 0 °C
ΔT = 30.0 °C
The specific heat capacity of water (c) is 4.18 J/g°C.
Now, we can calculate the heat absorbed by the resulting water:
Q = mcΔT
Q = 13.2 g * 4.18 J/g°C * 30.0 °C
To find the total heat absorbed by the ice cube and resulting water, add the two calculated values:
Total heat absorbed = Heat absorbed by the ice cube + Heat absorbed by the resulting water
I'll leave it to you to do the calculations and determine the final answer.